Question

Angle between the lines x+3=0 and y+7=0

Answer 1

Answer on Question #74147 – Math – Analytic Geometry

Question

Angle between the lines $x + 3 = 0$ and $y + 7 = 0$

Solution

The angle $\theta$ between the lines having slope $m_1$ and $m_2$ is given by

$$\tan \theta = \pm \frac{m_2 - m_1}{1 + m_1 m_2}$$

In our problem we have

$$x + 3 = 0 \Rightarrow x = -3, \text{ Vertical line}$$ $$y + 7 = 0 \Rightarrow y = -t, \text{ Horizontal line}$$

Then lines are perpendicular.

Therefore, the angle between the lines $x + 3 = 0$ and $y + 7 = 0$ is $90{}^\circ$.

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